Assuming that only area-level auxiliary information is available, we compare the weighted sample means \(\hat{\theta }_i^{\mathrm {d}}\)  from (REF ), the regression-synthetic estimators \(\hat{\theta }_i^{\mathrm {S}}\)  by (REF ), their initial compositions (REF ), and the compositions \(\hat{\theta }_i^{\mathrm {Cb}}\)  from (REF ) with EBLUPs based on the Fay–Herriot model [1]}. The later predictors are evaluated using the function mseFH from R package sae [2]}, where we use the smoothed variances \(\hat{\psi }_i^{\mathrm {s}}\)  and estimate the variance of the random area effects choosing the method of moments. The same function evaluates the MSE estimators for EBLUPs, and we compare them with MSE estimators (REF ) applied to design-based compositions (REF ) and (REF ). The results for the proportions of the unemployed and employed are presented in Tables REF  and REF , respectively.
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